Abstract
In this paper, we propose two original and efficient approaches for enforcing singleton arc consistency. In the first one, the data structures used to enforce arc consistency are shared between all subproblems where a domain is reduced to a singleton. This new algorithm is not optimal but it requires far less space and is often more efficient in practice than the optimal algorithm SAC-Opt. In the second approach, we perform several runs of a greedy search (where at each step, arc consistency is maintained), possibly detecting the singleton arc consistency of several values in one run. It is an original illustration of applying inference (i.e., establishing singleton arc consistency) by search. Using a greedy search allows benefiting from the incrementality of arc consistency, learning relevant information from conflicts and, potentially finding solution(s) during the inference process. We present extensive experiments that show the benefit of our two approaches.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Apt, K. R. (2003). Principles of constraint programming. Cambridge: Cambridge University Press.
Bartak, R., & Erben, R. (2004). A new algorithm for singleton arc consistency. In Proceedings of FLAIRS’04 (pp. 257–262).
Bessiere, C. (1994). Arc consistency and arc consistency again. Artificial Intelligence, 65, 179–190.
Bessiere, C., & Debruyne, R. (2004). Theoretical analysis of singleton arc consistency. In Proceedings of ECAI’04 workshop on modelling and solving problems with constraints (pp. 20–29).
Bessiere, C., & Debruyne, R. (2005). Optimal and suboptimal singleton arc consistency algorithms. In Proceedings of IJCAI’05 (pp. 54–59).
Bessiere, C., & Debruyne, R. (2008). Theoretical analysis of singleton arc consistency and its extensions. Artificial Intelligence, 172(1), 29–41.
Bessiere, C., & Régin, J. (2001). Refining the basic constraint propagation algorithm. In Proceedings of IJCAI’01 (pp. 309–315).
Bessiere, C., Régin, J. C., Yap, R., & Zhang, Y. (2005). An optimal coarse-grained arc consistency algorithm. Artificial Intelligence, 165(2), 165–185.
Boussemart, F., Hemery, F., Lecoutre, C., & Sais, L. (2004). Boosting systematic search by weighting constraints. In Proceedings of ECAI’04 (pp. 146–150).
Chmeiss, A., & Sais, L. (2000). About the use of local consistency in solving CSPs. In Proceedings of ICTAI’00 (pp. 104–107).
Debruyne, R., & Bessiere, C. (1997a). From restricted path consistency to max-restricted path consistency. In Proceedings of CP’97 (pp. 312–326).
Debruyne, R., & Bessiere, C. (1997b). Some practical filtering techniques for the constraint satisfaction problem. In Proceedings of IJCAI’97 (pp. 412–417).
Debruyne, R., & Bessiere, C. (2001). Domain filtering consistencies. Journal of Artificial Intelligence Research, 14, 205–230.
Dechter, R. (2003). Constraint processing. San Francisco: Morgan Kaufmann.
Frost, D., Dechter, R., Bessiere, C., & Régin, J. C. (1996). Random uniform CSP generators. http://www.lirmm.fr/~bessiere/generator.html.
Lecoutre, C. (2008). Optimization of simple tabular reduction for table constraints. In Proceedings of CP’08 (pp. 128–143).
Lecoutre, C. (2009). Constraint networks: Techniques and algorithms. New York: ISTE/Wiley.
Lecoutre, C., & Cardon, S. (2005). A greedy approach to establish singleton arc consistency. In Proceedings of IJCAI’05 (pp. 199–204).
Lecoutre, C., & Hemery, F. (2007). A study of residual supports in arc consistency. In Proceedings of IJCAI’07 (pp. 125–130).
Lecoutre, C., & Prosser, P. (2006). Maintaining singleton arc consistency. In Proceedings of CPAI’06 workshop held with CP’06 (pp. 47–61).
Mackworth, A. K. (1977a). Consistency in networks of relations. Artificial Intelligence, 8(1), 99–118.
Mackworth, A. K. (1977b). On reading sketch maps. In Proceedings of IJCAI’77 (pp 598–606).
Mohr, R., & Henderson, T. C. (1986). Arc and path consistency revisited. Artificial Intelligence, 28, 225–233.
Mohr, R., & Masini, G. (1988). Good old discrete relaxation. In Proceedings of ECAI’88 (pp. 651–656).
Prosser, P. (1996). An empirical study of phase transitions in binary constraint satisfaction problems. Artificial Intelligence, 81, 81–109.
Prosser, P., Stergiou, K., Walsh, T. (2000). Singleton consistencies. In Proceedings of CP’00 (pp. 353–368).
Sabin, D., & Freuder, E. C. (1994). Contradicting conventional wisdom in constraint satisfaction. In Proceedings of CP’94 (pp. 10–20).
Sabin, D., & Freuder, E. C. (1997). Understanding and improving the MAC algorithm. In Proceedings of CP’97 (pp. 167–181).
Ullmann, J. R. (2007). Partition search for non-binary constraint satisfaction. Information Science, 177, 3639–3678.
Zhang, Y., & Yap, R. (2001). Making AC3 an optimal algorithm. In Proceedings of IJCAI’01 (pp. 316–321).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bessiere, C., Cardon, S., Debruyne, R. et al. Efficient algorithms for singleton arc consistency. Constraints 16, 25–53 (2011). https://doi.org/10.1007/s10601-009-9080-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10601-009-9080-5